ESDU 97030:2011

INTRODUCTION

This Item is the third in a sequence dealing with the VGK
aerofoil method. The Item describes the use of VGK to estimate a
separation boundary for two-dimensional aerofoils in transonic flow
in terms of lift coefficient and freestream Mach number. The basis
of the Item is the method described in Transonic Data Memorandum
No. 81020 (Reference 1), and the separation boundary corresponds to
conditions on the upper surface of the aerofoil for which the shock
strength and the adverse pressure gradient(s) are sufficiently
severe for the trailing-edge pressure coefficient, relative to its
trend with increasing lift coefficient or Mach number in attached
flow, to have decreased by 0.05.

The full description of the underlying principles and
limitations of the method, which is essentially based on
‘calibrating' VGK results against experimental data, is given in
Reference 1. The present describes only the detailed organisation
of the computation involving VGK runs so as to obtain points on the
separation boundary in a reliable and efficient way. For a
description of the principles and typical results of the VGK
method, reference should be made to Part 1 of the sequence of Items
(ESDU 96028), whilst details of the various types of VGK runs, the
naming convention and functions of various files and the use of the
program VGKCON (the VGK ‘control' program) are given in Part 2
(ESDU 96029).

The estimation of a single point on an aerofoil separation
boundary requires a number of VGK runs to be performed. These runs
constitute a ‘sequence'. The first of such runs would normally
relate to a combination of Mach number and incidence at which there
were significant positive margins in terms of both the
‘shock-upstream criterion' and the ‘trailing-edge criterion'. These
criteria are reproduced from Reference 1 as Figures 1a and 1b,
where examples of positive margins are indicated. Successive VGK
runs in the sequence are carried out at the same Mach number, with
various values of incidence, until two successive VGK runs yield
one or other of the margins sufficiently close to zero. (Two
successive runs are required so as to ensure that VGK has
adequately converged – see Section 4.) The values of Mach number
and lift coefficient of the last VGK run in the sequence then
constitute the single point on the separation boundary. The
sequence of VGK runs is controlled by a Fortran program, SEPCON.
This program produces a record of the flow conditions and criterion
margins of the VGK runs, and at each stage in the sequence produces
the files necessary for the next VGK run. The organisation of the
commands to execute the VGK and SEPCON programs in a batch file is
described in Section 5. Procedures for obtaining a number of points
on an aerofoil separation boundary are also presented.

Estimated separation boundaries obtained using the present
method are presented and compared with observed results in Section
6.